On the Construction of Nonbinary Quantum BCH Codes

Author

Gadioli La Guardia, Giuliano

Author_Institution

Dept. of Math. & Stat., State Univ. of Ponta Grossa, Ponta Grossa, Brazil

Volume

60

Issue

3

fYear

2014

fDate

Mar-14

Firstpage

1528

Lastpage

1535

Abstract

Four quantum code constructions generating several new families of good nonbinary quantum nonprimitive nonnarrow-sense, Bose-Chaudhuri-Hocquenghem codes, are presented in this paper. The first two are based on Calderbank-Shor-Steane (CSS) construction derived from two nonprimitive Bose-Chaudhuri-Hocquenghem codes. The third one is based on Steane´s enlargement of nonbinary CSS codes applied to suitable subfamilies of nonprimitive nonnarrow-sense Bose-Chaudhuri-Hocquenghem codes. The fourth construction is derived from suitable subfamilies of Hermitian dual-containing nonprimitive nonnarrow-sense Bose-Chaudhuri-Hocquenghem codes. These constructions generate new families of quantum codes whose parameters are better than the ones available in the literature.

Keywords

BCH codes; Bose-Chaudhuri-Hocquenghem codes; CSS construction; Calderbank-Shor-Steane construction; Hermitian dual-containing nonprimitive nonnarrow-sense codes; nonbinary quantum BCH codes construction; Cascading style sheets; Context; Generators; Indexes; Linear codes; Polynomials; Quantum mechanics; Bose–Chaudhuri–Hocquenghem codes; cyclotomic coset; quantum codes;

fLanguage

English

Journal_Title

Information Theory, IEEE Transactions on

Publisher

ieee

ISSN

0018-9448

Type

jour

DOI

10.1109/TIT.2014.2298137

Filename

6702478